Adjoint Based Topology Optimization in Nonlinear Magnetostatics Application to Hall Effect Thrusters

In this paper, density based topology optimization is considered in nonlinear magnetostatics. Previously, topology optimization in linear magnetostatics was formulated to design Hall-effect thrusters and it was solved using gradient based solvers. In that previous version, the gradient information was provided by the continuous adjoint method. Herein, the adjoint approach is updated in order to take into account the saturation aspect of materials. This new version of the adjoint method is implemented and compared to a finite difference approach. The comparison shows that the so-developed adjoint based gradient information in non linear magnetostatics is accurate and ready for use to solve a topology optimization design problem. Hence, a Hall-effect thruster topology optimization problem is solved in both linear and non-linear cases and a comparative description of the found designs will be presented.